- Clearly identify the solution. Show your work. - You are encouraged to type your solutions. It is your responsibility to make sure that the solution is legible, correctly uploaded and viewable through the system. - You may discuss the problems with classmates but you are required to write down your own solutions. Problem 1. For each of the following production functions calculate the marginal product with respect to each factor, the marginal rate of technical substitution and graph the cor- responding isoquants. Evaluate whether the marginal product of each factor is increasing, constant or decreasing (over any relevant ranges). Evaluate whether the returns to scale. 1. f(K,L)=2K + VL 2. f(k,L) =min{2K, K + L} 3. f(k,L) = K + min{K, L} 4. f(K,L) = max{K,2L} Problem 2. For each of the production functions in the previous problem, write down and solve the cost minimization problem of a firm with that technology of production subject to producing at least units. Problem 3. Write down and solve the profit maximization problem of a firm with technology of production f(K,L) = KY4L1/2 selling at price p per unit. Write down the firm's supply curve